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3 years ago

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A single person pays $3,100 in income taxes on a gross income of $38,000. How much would a single person be expected to pay if h

is gross income is $44,000? (Assume both incomes are in the same tax bracket.)

1 answer:

elixir [45]3 years ago

5 0

I/44000=3100/38000

i=3100(44000)/38000

i=$3589.47 (to nearest cent)

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Find two positive numbers whose difference is 30 and whose product is 2584.

kvasek [131]

Answer:

$38$ and $68$ .

Step-by-step explanation:

Let $x$ be the smaller one of the two number.

$x$ must be a positive integer. The other number would be $(x + 30)$ .

The question states that the product of the two numbers is $2584$ . In other words:

$x\, (x + 30) = 2584$ .

Rearrange this equation and solve for $x$ :

$x^{2} + 30\, x - 2584 = 0$ .

The first root of this quadratic equation would be:

$\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}$ .

Similarly, the second root of this quadratic equation would be:

$\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}$ .

Since the question requires that both numbers should be positive, $x > 0$ . Therefore, only $x = 38$ is valid.

Hence, the two numbers would be $38$ and $(38 + 30)$ , which is $68$ .

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Find the distance from the point (4,2) to the line y= −2.

riadik2000 [5.3K]

Answer:

The distance is 4.

Step-by-step explanation:

The shortest distance from the point (4,2) to the line y=-2, in this case, would be a straight line perpendicular to y=-2.

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At this point the distance is:

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madreJ [45]

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45°

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Step-by-step explanation:

Let the measure of one angle be x

So, measure of its supplementary angle = 3x

$\implies \: x + 3x = 180 \degree \\ \\ \implies \: 4x = 180 \degree \\ \\\implies \: x = \frac{ 180 \degree}{4} \\ \\\implies \: x = 45 \degree \\ \\ \implies \: 3x = 135 \degree$

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2 years ago

This figure is made up of a quadrilateral and a semicircle.

Arturiano [62]

Answer:

The correct option is B. The area of the figure is 40.4 units².

Step-by-step explanation:

The line AB divides the figure in two parts one is a rectangle and another is semicircle.

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The length of AD is

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Since AB=AD, therefore ABCD is a square. The area of the of square is

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The area of square is 29 units².

The area of a semicircle is

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Since AB is the diameter of the semicircle, therefore the radius of the semicircle is

$r=\frac{d}{2}=\frac{\sqrt{29}}{2}$

The area of the semicircle is

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Answer:

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Step-by-step explanation:

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